Second-harmonic generation from a thin cylindrical layer: II. Analysis of the solution

The solution is analyzed for the problem of the second harmonic generation by a plane electromagnetic wave with elliptical polarization from a thin optically nonlinear layer on the surface of a cylindrical particle of finite size. A graphical analysis of the solution is carried out by constructing three-dimensional radiation patterns characterizing the spatial distribution of the second-harmonic radiation power and its polarization. It is found that for small radii of the base of the cylindrical particle, each anisotropy coefficient corresponds to its own individual shape of the radiation pattern. Increasing the height of the cylindrical particle leads to flattening of the radiation pattern. More than 20 mathematical properties of the solution are found, which characterize symmetries of the second harmonic field distribution. Individual properties are illustrated in radiation patterns.